contracting with spatial externalities and agency problems the case of retail leases

ELSEVIER Regional Science and Urban Economics 25 (1995) 355-372

Contracting with spatial externalities and agency problems

The case of retail leases

T h o m a s J. Micel i a'*, C .F . S i rmans b

aDepartment of Economics, University of Connecticut, Monteith Building, U-63, 34I Mansfield Road, Storrs, CT 06269-1063, USA

hDepartment of Finance, University of Connecticut, School of Business Administration, U-41RE, Room 426, 368 Fairfield Road, Storrs, CT 06269-2041, USA

Received April 1993; final version received June 1994

Abstract

This paper examines leasing arrangements between a shopping center landlord/ developer and individual stores in the presence of inter-store shopping externalities. The problem is to design individual leases so that (i) stores internalize inter-store externalities, and (ii) the landlord does not underprovide marketing effort that is beneficial to all stores. We show that the key element for achieving these goals is the ability of the landlord to cancel the leases of stores whose sales fail to achieve a target level. Such cancellation, or ' recapture' , clauses are common in commercial leases. We also show that in the absence of such a clause, familiar types of commercial leases fail to achieve the above objectives.

Keywords: Spatial externalities; Agency costs; Leases

JEL classification: L14; R12

I . Introduction

A recen t d e v e l o p m e n t in the economics of con t rac t s dea ls with the p r o b l e m of c o m m o n agency , def ined as a s i tua t ion in which mul t ip le p r inc ipa l s con t r ac t with a single agent . A n i m p o r t a n t resul t ar is ing f rom this

* Corresponding author.

0166-0462/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0166-0462(94)02079-5

356 T.J. Miceli, C.F. Sirmans ! Reg. Sci. Urban Econ. 25 (1995) 355-372

literature is that a group of principals with inter-dependent interests can coordinate their behavior through the common agent, x In this paper we view the leasing of retail space in a shopping center as an example of common agency. That is, we view shopping center leases as providing a means whereby individual stores can contract with a common landlord/developer in an effort to internalize 'demand externalities' present in spatially concen- trated business locations. 2

Shopping centers have become a pervasive feature of the urban land- scape. For example, the National Research Bureau, a firm that collects data on shopping centers nationwide, reports in their Spring 1992 newsletter, Shopping Center Directions, that there were 37,975 shopping centers in the United States in 1991. These centers contain 4586 million square feet of space and accounted for 716,913 million dollars of retail sales. Although shopping centers have been blamed, at least in part, for the decline in downtown business districts in many cities 3 their success bespeaks the economic benefits they provide consumers in the form of economies in shopping costs, relief from downtown traffic congestion and parking problems, and other amenities. These benefits in turn translate into higher profits for businesses locating in shopping centers.

The success of a shopping center, however, depends on the developer's ability to exploit its unique feature: the spatial concentration of a diverse array of stores. Because of the close proximity of stores, a customer attracted to the center can visit multiple stores at very low marginal cost. This creates an inter-store externality in that the profit of each store depends in part on how many customers the other stores attract. The success of the center therefore depends on the extent to which stores can internalize these externalities.

If transacting were costless, internalization of inter-store externalities could be accomplished through pairwise contracting among the stores aimed at efficiently setting each store's hours, advertising policy, contributions to common area maintenance, and the like. In the presence of transaction costs, however, a cheaper alternative might be for a single agent specializing in management (e.g. a landlord/developer) to contract with each store for the purpose of coordinating their decision-making and maintaining common areas. At the same time, however, such an arrangement creates another potential problem: if the value of the shopping center is to be maximized, the landlord/developer must not behave opportunistically; for example, by undermaintaining common areas or underinvesting in advertising. There-

See Bernheim and Whinston (1985) and Stole (1991). 2 For a good review of the economics of business location, see Stahl (1987). 3 See, for example, Glaberson, (1992).

T.J. Miceli, C.F. Sirmans / Reg. Sci. Urban Econ. 25 (1995) 355-372 357

fore, we also show how shopping center leases can resolve this agency problem between each store and the landlord/developer. 4

The analysis is organized as follows. Section 2 develops a simple model of a shopping center in which the profit of each store depends on its own sales effort, the sales effort of all the other stores, and the effort of the landlord/developer. Section 3 then examines a class of retail contracts that induces optimal effort by all stores as well as the landlord. The cases of both stochastic and non-stochastic sales are examined. The key element of the efficient contracts in each case is the ability of the landlord/developer to cancel the leases of stores whose sales fail to achieve a target level. Section 4 shows that a common type of shopping center lease - a breakpoint-overage l e a s e - fails to achieve optimal effort in the absence of a cancellation provision. Section 5 then explicitly considers the percentage-of-sales feature of overage rents and shows that they capture some features of optimal risk-sharing contracts but depart from them in other respects. Finally, Section 6 concludes.

2. The model

Consider a shopping center consisting of n retail stores, indexed by i = 1, 2 , . . . , n, and a single landlord/developer (henceforth referred to simply as the landlord), denoted by L. Each store i generates revenue that depends positively on the sales effort of the store's own manager, 5 ei, the effort of the managers of all the other stores, e_ i, and the effort of the landlord, m. Store i's own effort increases its expected sales through advertising, better merchandise selection, and attractive displays, while the effort of other stores increases the expected sales of store i as a result of inter-store externalities. 6

The effort of the landlord consists of several activities, including de- termining the best site and design for the center, choosing the mix of tenants, conducting advertising, and maintaining common areas. In effect, the landlord provides a public good for all of the tenants in the center. 7

4This situation thus resembles the common agency problem examined in Bernheim and Whinston (1985) where the landlord is a common agent, but at the same time it resembles the problem of team production studied in Holmstrom (1982) where the landlord is the principal and the stores comprise the team.

5 We do not distinguish between owners and managers of the stores. 0 Externalities of this sort are obviously present in downtown business districts as well, but

the purpose of this paper is to argue that contractual arrangements in shopping centers are specifically designed to exploit them efficiently.

7 In downtown business districts, one might view the local government or a chamber of commerce as performing this function.

358 T.J. Miceli, C.F. Sirmans / Reg. Sci. Urban Econ. 25 (1995) 355-372

While the landlord's activities in this regard are multi-faceted, their ultimate impact is to increase the sales of tenant stores. Thus, for simplicity, we view the landlord as choosing a single variable, m, to be interpreted as effort, which positively affects the sales of each store.

Formally, we write the expected sales of store i (net of the cost of merchandise) as

S i = S i ( e o e i , m ) , i = 1 . . . . . n , (1)

where S i is increasing in each of its arguments. Each store incurs the cost of its own effort, c i ( e i ) , which is an increasing, convex function, and it pays rent, Ri, to the landlord. 8 Store i's expected profit per period is thus given by

7"t" i = S i ( e i , e _ i , m ) - c i ( e i ) - R i , i = 1, . . . , n . (2)

The per-period profit of the landlord consists of the aggregate rent paid by the n tenants less his cost of effort, or

rc L = ~ R i - c L ( m ) . i - I

The aggregate profit per period generated by the shopping center is given by the sum of the tenants' profits plus the landlord's profit. Denote this quantity by J, where

J = ~ [Si (e i, e_ i, m ) - c,(ei) l - eL(m ) . (4) i - 1

Note that the rents drop out of this expression since they are simply transfer payments from the tenants to the landlord. The efficient level of effort by the n stores and the landlord are found by maximizing J. The first-order condition for e i is given by

' = 0 OS// Oe i - c i , / t

or

as, asj i/~,,0e--+~~e, - c ' / = 0 ' i = 1 . . . . . n , (5)

and the first-order condition for m is given by

In actual leases, fixed expenses such as taxes and common area charges are 'passed through' to tenants. We abstract from these costs here.

T.J. Micefi, C.F. Sirmans / Reg. Sci. Urban Econ. 25 (1995) 355-372 359

~ O S i / O m - c~ = 0. (6) i = 1

The inter-store externalities are captured in Eq. (5) by the fact that the marginal benefit for store i's effort includes not only the effect of e i on its own sales (OSi/ae ~ > 0), but also the effect on the sales of all the other stores ( 2 j ~ i OSj/Oeg 1> 0). Similarly, Eq. (6) captures the public good nature of the landlord's effort given the positive impact of m on the sales of all the stores. Denote the solutions to (5) and (6) e*( i = 1 , . . . , n) and m*, respectively. The optimal solution will serve as the benchmark for evaluating the equilibrium choices of the parties under the leasing arrangements examined below.

3. Efficient contracts

We begin by showing that neither fixed rent leases nor percentage-of-sales leases will induce stores to internalize the inter-store externalities described above. With fixed rent leases, stores will only consider the impact of their effort on their own sales. Specifically, e i will be chosen to maximize (2), yielding the first-order condition aSi /Oe i - c ' i =0 . Comparing this to (5) shows that stores take too little effort. Straight percentage rents only exacerbate the problem by requiring the store to pay a portion bi of its sales

' = 0. 9 Given in rent. In this case, Ri = b i S i and e~ solves ( 1 - b i )aS i / ae i - c i these results, we therefore consider the role of cancellation, or minimum sales, clauses in forcing stores to internalize inter-store externalities. We also show that such clauses will induce landlords to invest efficient effort, assuming that stores compete for space in shopping centers. We demonstrate these results both when sales are non-stochastic and when they have a random component .

3.1. Non-s tochas t ic sales

First, consider the marketing effort of individual stores. The landlord's problem is to design a set of contracts so that in the Nash equilibrium, each store chooses the jointly optimal effort level as determined by (5). It turns out that this is possible if we assume that stores compete to locate in the shopping center, and if they make bids in terms of minimum sales, S r Note

Brueckner (1993) also shows the inefficiency of straight percentage rents. Below, we examine percentage rents that include a fixed base rent and demonstrate their inefficiency as well.


the impact of bidding in terms of sales. Although the effort of individual stores is unobservable, a store's commitment to a minimum sales level implies a minimum effort level, given that all other stores are making similar commitments (in a Nash equilibrium), and given the absence of randomness in sales. That is, store i 's promise of S i ( e i, * * * e _ i , m )>~Si(e*,e*_i,m*)=--S i is equivalent to a promise of e i/> e~ (note the assumption that the landlord also chooses optimal effort, m*, a result that we establish below). Following the formal analysis, we comment on the enforcement of the store 's commitment to a minimum sales level. If stores also bid in terms of rent, R i, then the set of winning pairs (Si, Ri) across all stores maximizes the profit of the landlord in (3), subject to the condition that each store just covers its opportuni ty cost, rr °.

The foregoing discussion implies that the optimal choices of ei, R i, and m solve

max ~ R i - CL(m ) + ~ a i [ S i ( e i , e _ i , m ) - c i ( e i ) - R i - zr°l, (7) i i

where A i is the Lagrange multiplier on the profit constraint for store i. The first-order conditions for this problem for e i, R i, m , and A i, respectively, are given by

E ) t j ( o s j / o e i ) - A ic ' i (e i ) = 0 , i = 1 , . . . , n , (8) /

1 - h i = O , i = l , . . . , n , (9)

- c [ ( m ) + ~ A i ( 3 S i / O m ) = O, (10) i

S i - - c i ( e i ) - R i - rr~ = O, i = 1 , . . . , n . (11)

(9) implies that A i = 1, all i. Substituting this into (8) and (10) yields conditions (5) and (6), respectively. Thus, all n stores as well as the landlord internalize the inter-store externalities, and the jointly optimal solution is attained.

Fig. 1 illustrates this solution. The impact of the promise of a minimum sales level for store i, S,*., is illustrated for the case where its individual profit-maximizing effort in the absence of a sales commitment , e ' i, is less than e*. As shown above, this will be true under both a fixed rent lease and a percentage-of-sales lease. 1° The graph shows that store i maximizes its

* given * and m*. profit, subject to S i >-S*, by choosing e i e i

~°Brueckner (1993) has shown that e,* can be achieved by a rental contract of the form R, = a i - biS~, b~ > 0, which in effect pays store i a percentage of sales subsidy. However, such contracts are not observed in practice so we do not consider them here.

T.J. Miceli, C.F. Sirmans / Reg. Sci. Urban Econ, 25 (1995) 355-372 361

~r S i S i (e i e*_i. rn*)

I

7--7- 'S Cei'e-* I I

I 1 e~ el* e i

I

- c i ( e i) Si(e i ,e*_ i .n~ - c i ( e i ) - R i

Fig. 1.

Fig. 1 also shows why the landlord chooses the jointly optimal level of m. Note that the impact of increasing m is to shift up the sales and profit curves for each store by the amount OSi/Om. However, the landlord can fully capture this increase in each store's sales because the maximum R i that store i will bid increases by the same amount. As a result, each store remains at its opportunity profit level, ~r °, and the landlord fully internalizes the joint benefits of his effort. Thus, he chooses optimal effort, m*. tl

It is useful to compare the results obtained here with those obtained in different contexts by Holmstrom (1982) and Danzon (1983). Holmstrom considers the case of team production where n agents contribute effort to the production of a single output. Thus, an 'inter-agent externality' of the sort considered here exists, but the difference is that only a single, non- separable output is observed. Nevertheless, Holmstrom shows that when output is non-stochastic, the first-best effort by all agents can be obtained by a payment scheme that penalizes all agents if a target output (the joint optimum) is not achieved. One interpretation of this scheme is that it is a threat to discontinue cooperation (Holmstrom, 1982, p. 327).

Similarly, the landlord can enforce each store's promise of a minimum sales by failing to renew leases for individual stores who do not achieve their minimum sales level. Clauses of this sort, often referred to as ' recapture clauses,' are common in shopping center leases. A typical clause might read:

~ This result is similar to that obtained by Bernheim and Whins ton (1985), who show that when compet ing firms employ a common market ing agent, they are able to implement the collusive solution. See especially pp. 275-276.

362 T.J. Miceli. C.F. Sirmans / Reg. Sci. Urban Econ. 25 (1995) 355-372

'Landlord may terminate this lease if tenant 's gross sales in each year after the first do not exceed $300,000" (Senn, 1990, p. 170). 12 As Senn (1990, p. 178) notes, "insufficient sales [reveal] a tenant 's inability to draw customers and thus to augment the sales of fellow tenants ."

The analysis in Danzon (1983) concerns the effort of an attorney on behalf of a client under a contingent fee arrangement. Although a common argument in favor of contingent fees is that they induce attorneys to work in the interests of their clients, the fact that the attorney only receives a fraction of any recovery prevents him from choosing the client's most preferred effort level (this is demonstrated in the same way that we showed the inefficiency of percentage rents above). Danzon argues, however, that if at torneys bid for clients in terms of the percentage rate and the expected recovery, then attorneys will commit themselves to optimal effort) 3 Compe- tition among lawyers for clients and concern for reputation enforces this commitment .

Danzon 's conclusions regarding contingent fees imply that the analysis of shopping center contracts would hold equally well for percentage-of-sales leases, where tenants compete in terms of minimum sales levels and percentage rates. In particular, it is easy to show that the above analysis is unaffected by writing R i = biS i and choosing b i optimally instead of Ri. Thus, the conclusions of this section are consistent with conventional percentage-of-sales leases, although it is important to note that they do not require leases to be in this form. In contrast, Brueckner 's (1993) results suggest that percentage leases cannot be optimal. The difference is that he does not allow stores to compete based on minimum sales commitments .

3.2. S tochast ic sales

Up to now we have assumed that there is no randomness in sales. In this section, we examine efficient contracts when sales have a random component.

When sales were non-stochastic, the failure of a store to achieve its target sales demonstra ted with certainty that it was shirking, given optimal effort by all other stores and the landlord. When sales have a random component , however, this is no longer true. Uncertainty thus complicates the usefulness of sales targets as a means for enforcing optimal effort by stores. Neverthe-

~2 Also see Friedman (1983, p. 196). A recent federal court decision in Hawaii, however, suggested that in some circumstances, non-renewal of a lease for inadequate sales will be interpreted as illegal price-fixing. See Bertleys Town and Country Shops, Inc. v. Dillingham Corp., 530 R. Supp. 499 (1982).

~ A similar story applies to real estate brokers, who compete on the basis of listing prices as well as commission rates.


less, such a me thod can still be used at least to approximate the joint op t imum. The derivat ion of this result closely follows Ho lms t rom ' s (1982) analysis of the case of team product ion under uncertainty.

No te first that the condit ions for the joint op t imum given by (5) and (6) are unaffec ted by the in t roduct ion of uncer ta inty if we rewrite them in terms of expec ted sales, ESi, and assume risk neutrali ty of all parties. '4 Second, it will be necessary to specify a distribution function of sales for store i and how that distr ibution is affected by effort. Thus, we write the condit ional distr ibution of S i as FI(S i, e i, e_ i, m), where OF,/OS i =-fi > 0 , 3Fi/Oe < 0 , and OF~/Om < 0 . The latter two condit ions simply say that greater effort by all s tores and the landlord shift the distribution r ightward toward higher values o f Si. '5

In this setting, we again consider a contract for store i that specifies a rent R i and a min imum sales level SI'. If store i 's actual sales are at least S~/ in any per iod, it can remain in the shopping center , but if sales fall below S' / ,

its lease will be cancelled. With uncertain sales, however , these ou tcomes can only be specified probabilistically. In particular, for given (S~},e~,e i , m ) , the probabil i ty that store i will remain is given by 1 - ~(S~}, e i, e ~ , m), and the probabil i ty that its lease will be cancelled is given by Fi(SI ~, ei, e i, m ) ( to conserve on nota t ion, we will hencefor th write these simply as 1 - F i and F/). If the s tore 's lease is cancelled, we assume that it earns its next-best per-per iod profit, ~r~i ~, in all future periods.

Given this specification, the present value of a s tore 's expected profits over an infinite horizon can be written

o 7 7 i 7r,.

7r i = E S i - c,(ei) - R, + (1 - F i ) ~ T - 7 + F i r

- - F i ~ - + r [ E S , - c i ( e i ) - R i + i T , i = 1 . . . . . n . (12)

Store i takes the terms of the lease, (Ri, ~ S i ) , as given and chooses e i to maximize (12). The first-order condit ion is given by

Ovr, 3ES, 0F~/Oei [ES i - c,(ei) - R i - 7r'}l - c i ( e i ) = 0 (13) 3e i = Oe i F i + r

,4 The assumption of risk-neutrality greatly simplifies the analysis. If the parties are risk- averse, then optimal contracts will generally balance risk-sharing and incentives (Holmstrom, 1979). See the discussion of risk-sharing in the absence of incentive problems in Section 5 below.

'5 This characterization of uncertainty in sales is based on a sales function of the form S,(e, e i , m, 0i), where 0 i is a random variable. Following Holmstrom (1979. 1982), we suppress 0, and treat S, as a random variable with distribution F,(S , ,e ,e , m ) , which has the characteristics noted in the text.


where -OFi/ae i > 0. Thus, the second term on the right-hand side is positive if and only if the term in the square brackets is positive (we will return to this point below). Moreover, comparing (13) with (5) shows that, in order for e* to be a Nash equilibrium, this second term must be equal to Ej,~i(OESi/Oei) when (13) is evaluated at e* and m*. Note that the bracketed term in (13), which is the excess of store i's profits in the center compared with its next-best alternative, functions as a sort of 'penalty' paid by the store for shirking and being evicted. In this sense, the mechanism used here to maintain the incentives of stores is similar to that employed in the efficiency wage li terature) 6

Given the behavior of stores as dictated by (13), consider now the problem facing the landlord. He must choose the terms of each store's lease (the S7's and Rg's), as well as m, to maximize his profit (still given by (3)), subject to (13) and the condition that stores not vacate voluntarily in each period: E S ~ - c i - R ~ > 7r(~). ~7 Note the new feature of this problem as compared with the certainty case. Since sales are now random, a store cannot avoid eviction with certainty by choosing e*. Thus, the constraints S~ >I-S* in the certainty case are replaced by (13) with the landlord choosing the threshold sales level S~i ) for each store.

At this point, we need to make an assumption about the distribution functions for the S~. In particular, we assume that [aC/ae~l/F~--, o~, as S°---> 0 (the lower bound on Si). Intuitively, this assumption, which is also made by Holmstrom (1982 Assumption 2, p. 328), states that as S(~ ~, and hence, F,, become very small, the impact of store i's actions on the distribution of Si becomes easily discernible. 18 We further assume that this implies that the term -(aF~/aeg)/(F i + r) in (13) can be made large by lowering S~ ~, the sales threshold. This will be true provided that -(aFg/ae~)/r remains large as S~,)--~ 0. ~9 Given these assumptions, the term in square brackets can be made arbitrarily small while still maintaining incentives. As a result, the landlord can raise Rg while simultaneously lowering S~i ~ and ensure that the equilibrium effort level by stores remains optimal.

Formally, the landlord's problem as described above yields the following first-order conditions for e~, m, S~ ~, and R,, respectively:

Z ' E A~(OES~/ae~) - Azc~ + /x~(a"Trj/0ejae,) = 0 , i = 1 . . . . , n , (14) / /

- c ~ + ~ hi(aES,/Orn ) + ~ ix~(aZzr,/Oegam) = 0 , (15) i i

~ See, for example, Shapiro and Stiglitz (1984), and Akerlof and Yellen (1986). ~7 Note that this constraint is equivalent to ~r ~> ~r<~(1 + r)/r. t8 See Milgrom (1981) for formal details. ~'~ See Holrnstrom (1982, p. 329) for some intuition on this point.

T.J. Miceli, C.F. Sirrnans / Reg. Sci. Urban Econ. 25 (1995) 355-372 365

2 o (16) txi(O 7ri/OeiOS i ) = O , i = l . . . . . n ,

2 , (17) 1 - A ~ + ~ ( O 7 r i / a e i a R ~ ) = O , i - - 1 . . . . . n

along with the condition that

E S i - c i - R i > ~ T r ~ , i = 1 . . . . , n . (18)

In these conditions, ~i is the multiplier on constraint (13) (which was written as aTri/ae ~ = 0 in the Lagrangian to save notation).

Consider first condition (16). It is easy to show that the term in parentheses has the same sign as

0 [ - O F ~ / O e i ( E S i - c i - R ~ - T r ° ) ] (19) OS°i F i + r

If E S i - c i - R i > 1r °, our assumptions above regarding ]OFi/Oei[/(F i + r) imply that (19) is negative. This implies that i.t i = 0 (from (16)), in which case (13) is not binding. This result is due to the fact that the landlord can adjust S o to ensure that (13) holds. The fact that he can make this adjustment without cost (as indicated by (16)) means that (13) will not be binding with respect to his choice of m and Ri (i.e./.~ = 0 in (15) and (17)). 2o

Notice, however, that as the landlord raises Ri, (18) approaches equality. Thus, 10F//0e~I/(F, + r) must become very large to ensure that (19) remains non-zero, given that the efficient choice of the e~'s and rn require both that /x~ = 0 (i.e. that (13) is not binding) and that A i = 1 (i.e. that (18) is binding). (This follows by comparing (14) and (15) with (5) and (6).) Evidently, therefore, the landlord's desire to continue raising R~ until (18) holds with equality will ultimately conflict with the efficient choices of e~ and rn, thereby possibly preventing attainment of the first-best solution.

The role of the cancellation clause again is important here since the 'penalty' term in brackets in (13) is what maintains the proper incentives for stores. As noted, since this term approaches zero as (18) approaches equality, - ( a F / a e i ) / ( F , + r) must become very large, which implies that SI ~ must approach zero. Ironically, therefore, the probability of cancellation, F,, must also approach zero. Intuitively, this occurs because of our assumption above that as F~--~ 0, store i's effort has a more distinguishable impact on F,, and hence on sales. Alternatively stated, as F,--~ 0, store i perceives that its effort to reduce the expected cost of cancellation (as measured by the second term in (13)) becomes more productive.

Note that the results here resemble those obtained by Becker (1968) in the context of criminal punishment. In particular, Becket showed that when

20 This result relies on the assumption that the landlord can replace evicted stores without

cost.

366 T.J, Miceli, C.F. Sirmans / Reg. Sci. Urban Econ. 2,5 (1995)355-372

punishment takes the form of a fine, the optimal probability of apprehen- sion, p, should approach zero while the optimal fine, f, should be made sufficiently large so that their product, pf, maintains optimal deterrence. 2~ In the current context, this corresponds to lowering S~ (and hence Fi) while simultaneously raising R~ so that the second term in (13) remains constant (and equal to E j~ ~ESj/Oei).

In practice, of course, the probability of cancellation can never equal zero, just as the probability of apprehending criminals cannot equal zero, for then there would be no incentive for stores to act efficiently, or for individuals to refrain from commiting crimes, no matter how large the penalty. Consequently, as noted above, there generally will be a conflict between the landlord's desire to raise R~ and his ability to lower S °~ while maintaining optimal incentives, in which case the efficient solution can only be approximated.

Finally, we note that the particular form of R~ again played no role in the analysis. Thus, as in the certainty case, percentage-of-sales contracts are consistent with the results, but are not implied by them.

4. Breakpoint-overage contracts

Actual shopping center leases generally specify rents as having a base component and an overage which is calculated as a percentage of sales. 22. Specifically, stores i's rent is written as:

Ri = {a~ , Si < Si , (20) ae + bi(Si - S i ) , Si ~ Si ,

where

a~ = the base rent, b~ = the fraction of store i's sales paid as the overage rent, 0 < bi < 1, S~ = the breakpoint.

The overage rent is thus given by b~(S~- S~). The rent of store i thus depends on its own sales and three parameters: a i,

2t Also see Townsend (1979) for a similar result in a more general context (see especially pp. 275-278). Al though the probability of "pun i shment" approaches zero in both Becket ' s model and the current solution, the reasons are somewhat different. In Becker, p---~0 because it is costly to raise p (e.g. more police have to be hired), whereas here, F~--*0 is associated with main tenance of efficient effort by stores.

22 For an empirical analysis of shopping center leases having this form, see Benjamin et al. (1990). The use of percentage of sales as a method for computing rent is very common in commercial leases. For an early discussion of the function of percentage rents, see Note (1948).


b~, and Si. In most contracts of this sort, however, these parameters are related to one another as f o l l o w s : 23

a i °~' = b-~i" (21)

When this relationship holds, Si is referred to as the 'natural breakpoint' because the constant base rent ai and the ray defined by bfl i intersect at S~ (see Fig. 2). Thus, if the sales of store i fall below S~, it pays only the base rent, but if they are above S~, it pays a pure percentage hi s i (the latter follows by substituting (21) into the second line of (20)).

It is easy to show that such contracts, without a cancellation provision, will not elicit efficient effort from stores. To show this, we define C(Si, e, m) as the probability that S i < Si; that is, the probability that store i's sales fail to reach the breakpoint, in which case its rent is ai. On the other hand, with probability 1 -F~ its rent is given by bgS i. We therefore write its expected profit per period as

7r~ = ES~ - F,a~ - (1 - Fi)b~E[S i ]S~ >1 Si] - c~(e~)

= ES~ - F~a i - b~ f S~f dS, - ci(e~) Si

= E S , - b, _( ( S , - gs ) f dS, - c , (e , ) . (22)

Ft i

1 I /

/ / /

/ /

/ /

/ /

/ /

/

Fig. 2.

z3 See, for example, Senn (1990, p. 160).

his i

$i

368 T.J. Miceli, C.F. Sirmans / Reg. Sci. Urban Econ. 25 (1995)355-372

The optimal choice of effort by store i is thus the solution to

Orr,/Oe, = OES i /Oe i - b~ f (S, - S,)(Of/ Oe,) dS, - c ' i

S i

Since

: o . (23)

(S i - - g~)(a~/0e~) dS, > O,

S i

(23) results in too little effort compared with the joint optimum. This is not surprising since (22) implies that store i's rent is essentially a weighted average of a fixed rent and a percentage-of-sales rent, neither of which alone induces optimal effort. Thus, the contract in (20), along the restriction in (21), will not elicit optimal effort from stores in the absence of a cancellation clause.

It is possible to show that a breakpoint-overage contract in which ai > b i S ~

c a n induce optimal effort. Intuitively, a i > hiS i would create a discontinuous drop in the rent schedule in Fig. 2 at the breakpoint 4 . Thus, if the 4 were set at the efficient sales level, stores could be induced to choose optimal effort to avoid paying the higher rent if a i were set high enough or b~ were set low enough. Since contracts of this sort are rarely observed, however, we do not pursue this point here.

5. The role of percentage-of-sales contracts in risk-sharing

Although the contracts we have examined are all sales-contingent contracts in the sense that a store's rents and/or its right to remain in the center depended on its sales, none required percentage-of-sales rents per se. Thus, the analysis to this point does not provide a p o s i t i v e theory of percentage rents. In this section, we therefore examine the role of percentage rents as risk-sharing devices. 24

The theory of optimal risk-sharing is well known. 25 In the shopping center context, if we ignore incentives, then the optimal rent for store i, R i ( S i ) , solves the equation

2~ Brueckner (1993) includes a similar discussion. 25 See, for example, Borch (1962).

T,J. Miceli, C.F. Sirmans / Reg. Sci. Urban Econ. 25 (1995) 355-372 369

where UL(. ) and Ui(- ) are the utility of profit functions for the landlord and store i, respectively, and Ai is the multiplier on the constraint that store i achieve some reservation utility. It follows from (24) that z6

dRi UL~; dS, ULI.Y; + U',U~ " (25)

Given risk-aversion by both parties, 0 < d R i / d S i < 1. Notice further that as the landlord becomes relatively more risk-averse, dRi/dSi---~O, which corresponds to a fixed rent contract. On the other hand, as the tenant becomes more risk-averse, dR~/dS~---~ 1, which corresponds to a contract whereby the landlord in effect 'buys out ' the tenant. That is, the landlord pays the tenant a fixed amount in return for the right to retain all of his sales.

More generally, if both parties are risk-averse, they share the sales risk, and something like a percentage-of-sales contract emerges (although (25) implies that a f i xed percentage rate is optimal only if both parties have

• • 2 7 constant absolute risk-aversion). In addition, if stores differ in their degree of risk-aversion, percentage rates should differ across store types. In particular, stores that are more risk-averse should have higher percentage rates in order to shift more of the risk to the landlord. The sample of percentage rates in Table 1 provides some mild support for this argument. 2s For instance, the stores with the higher rates tend to be those that specialize in a particular product, whereas stores with lower rates tend to be variety- type stores. 29 This is consistent with optimal risk-sharing to the extent that the latter-type stores can more easily diversify sales risk.

However, Table 1 also reveals a problem with relying on risk-sharing alone to explain percentage rents. Note that the rates for all types of stores are quite low; for example, none is greater than 9%. This implies that stores are generally bearing much more of their sales risk than is the landlord, a

z6 See, for example, Mirrlees (1976) and Holmstrom (1979). 27 That is, dR~/dS~ is constant only if both -UL/U[ and -U"JU' i are constants. z8 The data in the table were taken from a survey of several national real estate firms

conducted by Buildings: The facilities construction and management magazine (January issues, 1985-1989). Each firm was asked to report the percentage rate for retail leases for over sixty types of stores. The stores listed in Table 1 were chosen to represent a typical tenant mix.

z9 We ran some simple regressions on the data in Table 1 and showed that the percentage rates differ significantly across different types of stores.

370 T.J. Miceli. C.F. Sirmans / Reg. Sci. Urban Econ. 25 (1995) 355-372

Table 1 Mean percentage rental rates for various types of stores 1985-1989

Year Type of store 1985 1986 1987 1988 1989

Grocery stores (chain) 1.36 1.38 1.40 1.29 1.38 Discount stores 1.54 2.08 2.00 1.68 1.38 Department stores 1.79 2.08 1.88 1.71 1.69 Drugstores (chain) 2.61 3.21 2.92 2.64 2.13 Variety stores 3.43 3.15 3.83 3.42 3.25

Clothing: Children's 5.71 5.50 5.64 5.79 5.67 Men's 5.14 5.33 5.71 5.50 5.42 Women's 6.00 6.25 6.08 6.00 6.00

Shoes: Men's 6.21 6.08 6.75 5.79 6.08 Women's 6.21 6.17 6.42 6.29 6.08

Other: Candy 8.25 8.36 8.50 9.00 7.57 Dry cleaning 7.00 7.50 7.58 7.42 7.20 Ice cream 8.08 8.75 8.92 8.50 8.17 Jewelry (exclusive) 6.75 7.00 7.00 7.43 6.92 Optical 7.50 7.50 7.83 7.07 4.43 Restaurants 6.43 6.42 7.17 6.96 7.58

Source: From a survey conducted each year of national retail leasing firms by Buildings: The Facilities Construction and Management Magazine.

result that seems inconsistent with one's intuition that the landlord, because he is dealing with a broad range of store types, can better diversify sales risk. In addition, the breakpoint feature of most leases imposes all of the downside sales risk on the store since the percentage rent only applies above the breakpoint. Again, this is inconsistent with a pure risk-sharing arrangement.

6. Conclusion

This paper has examined leasing arrangements in shopping centers between individual stores and a landlord/developer. The objective was to derive conditions under which retail leases can solve two fundamental economic problems inherent in shopping center design. The first is to induce individual stores to internalize inter-store externalities arising from the inter-dependence of store profits, and the second is to ensure that the landlord does not underprovide effort that benefits all stores. The results

T.J. Miceli, C.F. Sirmans i Reg. Sci. Urban Econ. 25 (1995) 355-372 371

showed that the key mechan i sm for achieving these object ives is the abili ty

of l andlords to cancel the leases of stores whose sales fall short of a target level. A l t h o u g h cancel la t ion clauses of this sort are a c o m m o n feature of actual retail leases, the analysis failed to explain fully o ther c o m m o n features , most no tab ly , the percentage-of-sales form of overage rents.

Acknowledgements

We thank John Quigley and two a n o n y m o u s referees for commen t s that

great ly improved this paper .

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contracting with spatial externalities and agency problems the case of retail leases

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